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If A = [(alpha,0),(1,1)]and B =[(1,0),(5...

If A = `[(alpha,0),(1,1)]`and B `=[(1,0),(5,1)]` find the values of `alpha` for which `A^(2)` = B.

A

1

B

-1

C

4

D

no real values

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `A = [{:(alpha, 0), (1, 1):}], B = [{:(1, 0), (5, 1):}]`
`rArr A^(2) = [{:(alpha, 0), (1, 1):}] [{:(alpha, 0), (1, 1):}] = [{:(alpha^(2), 0), (alpha+1, 1):}]`
Also given, `A^(2) = B`
`rArr [{:(alpha^(2), 0), (alpha+1, 1):}] = [{:(1, 0), (5, 1):}]`
`rArr alpha^(2) = 1 " and " alpha + 1 =5`
Which is not possible at the same time.
`therefore` No real values of `alpha` exists.
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